1 / 15

12.1

Parametric Equations. 12.1. Find the derivative. Parametric equations can be used to describe motion that is not a function. If f and g have derivatives at t , then the parametrized curve also has a derivative at t. The formula for finding the slope of a parametrized curve is:.

nero
Download Presentation

12.1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Parametric Equations 12.1

  2. Find the derivative.

  3. Parametric equations can be used to describe motion that is not a function. If f and g have derivatives at t, then the parametrized curve also has a derivative at t.

  4. The formula for finding the slope of a parametrized curve is: This makes sense if we think about canceling dt.

  5. The formula for finding the slope of a parametrized curve is: We assume that the denominator is not zero.

  6. To find the second derivative of a parametrized curve, we find the derivative of the first derivative: • Find the first derivative (dy/dx). 2. Find the derivative of dy/dx with respect to t. 3. Divide by dx/dt.

  7. Example:

  8. Example: • Find the first derivative (dy/dx).

  9. 2. Find the derivative of dy/dx with respect to t. Quotient Rule

  10. 3. Divide by dx/dt.

  11. Find the slope of the line tangent to the point on the circle:

  12. Find the slope of the line tangent to the point on the circle: What is the equation of the line tangent to the point on the circle? Point:

  13. Determine the concavity of the cycloid on the interval This is always negative so the graph is concave down.

  14. Homework Page 535 #16-25, 27-31 all

  15. Homework Page 535 #1-15 odd, 16-31 all

More Related